Thermodynamic equilibrium melting temperature

Thermodynamic equilibrium melting temperature Crystalline fraction Derivative of x,... 

Thermodynamic Equilibrium Melting Temperature of Polymer Crystals... 

However, all the literature results [84,85,86,101], and despite the extrapolation methods adopted, the thermodynamic equilibrium melting temperature of the p crystalline form in SPS was higher than that of the a form. On the basis of thermodynamic equilibrium, the higher value of the melting tempera-... 

Primary crystallization occurs when chain segments from a molten polymer that is below its equilibrium melting temperature deposit themselves on the growing face of a crystallite or a nucleus. Primary crystal growth takes place in the "a and b directions, relative to the unit cell, as shown schematically in Fig. 7.8. Inevitably, either the a or b direction of growth is thermodynamically favored and lamellae tend to grow faster in one direction than the other. The crystallite thickness, i.e., the c dimension of the crystallite, remains constant for a given crystallization temperature. Crystallite thickness is proportional to the crystallization temperature. 

Figure 1 also shows that plasticized polyvinyl chloride begins to flow at a lower temperature. This is to be expected in view of the fact that equilibrium melting temperature of polymer crystals is depressed by monomeric diluents. A statistical thermodynamic treatment by Flory (13), showed that this effect depends on the nature of the polymer, concentration of the diluent, and the degree of polymer-diluent interaction in the following manner ... 

True thermodynamic equilibrium refers to the phase in their most stable state, and for the crystalline polymer phase the most stable conformation is the fully extended one. The equilibrium melting temperature, T , corresponds to the melting of perfect crystals of infinite size with fully extended chains. The value of for a polymer is unique. Since the crystalline samples of polymers are made up of crystals of finite size in which the chains are folded and not fully extended, the experimentally determined melting temperature, is always lower than There is a strong dependence of T on the thickness of the crystalline lamella, / always increases with /. 

What is important to the present study is to examine the effect of PEC comonomer, not i-PS copolymer structure, on the thermodynamics of interaction with i-PS. Consequently, we limited crystallization temperatures to values less than 180 °C to Inhibit the Tb enhancement process. As can be seen from Figures 5 and 6, good straight lines, which appear to follow Equation 6, can be drawn through the solid data points corresponding to these lower crystallization temperatures, and reasonable equilibrium melting temperatures result from the intersection of these lines with the Tb = Tc lines for each blend fraction of PEC. 

The determination of the thermodynamic equilibrium melting point (T ) of the crystallizable component of the blends by means of the dependence of melting temperatures of isothermally crystallized samples (I m) on the temperatures of crystallization (T ) has shown that = 130°C for neat LLDPE and LLDPE/SBH blends (52). 

We have seen that the experimental determination of the melting temperature of pol3nneric systems, suitable for use in thermodynamic analysis, possesses several inherent difficulties concerned with both concept and technique. Some of the main problems have been pointed out in this paper and the procedures by which they could be overcome has been indicated. Hence there are obvious difficulties in determining the equilibrium melting temperature from polymer data, even admitting the extrapolative procedure. A more detailed discussion of this aspect of the problem will be taken up in a subsequent publication (32). 

In addition to the ambiguities inherent to the physical concept, the determination of thermodynamic quantities such as the latent heat and the volume change at the transition is often hampered by the fact that the crystalline state of chain molecules is quite complex. The polymer crystals are usually polycrystalline and coexist with the disordered amorphous domain. An accurate estimation of the equilibrium melting temperature defined for a perfectly aligned crystal requires great effort [5,18,19]. At the melting temperature, equilibrium usually exists between the liquid and somewhat imperfect crystalline phases. 

Polyethylene data are shown in Fig. 2.23. At the equilibrium melting temperature of 416.4 K, the heat of fusion and entropy of fusion are indicated as a step increase. The free enthalpy shows only a change in slopes, characteristic of a first-order transition. Actual measurements are available to 600 K. The further data are extrapolated. This summary allows a close connection between quantitative DSC measurement and the derivation of thermodynamic data for the limiting phases, as well as a connection to the molecular motion. In Chaps. 5 to 7 it will be shown that this information is basic to undertake the final quantitative step, the analysis of nonequilibrium states as are common in polymeric systems. 

The other thermodynamic method that can be used to determine A// involves the variation of the equilibrium melting temperature with applied hydrostatic pressure, p. The ClapeyrOTi equatimi... 

In contrast to the gel formation at these concentrations, it is well known,30 that from more dilute solution, the polymer will precipitate, or crystallize, in the form of isolated lamella-like crystallites. It is theoretically possible to prepare both the lamella-like crystallites and the gels, of the same molecular weight fraction, at the same undercooling. This possibility exists since there is only an imperceptible change between the equilibrium melting temperature for a concentration of about 0.1%, where the platlets form, and the higher concentrations typical of gel formation.24 Hence, a rationale or natural comparison can be made between the thermodynamic properties of the well-known lamella-like crystallites typical of dilute solution crystallization and those of the crystallites involved in the gel formation when both are crystallized at the same temperature. In Table I, a typical set of such data is given. 

Fig. 2.2. Two-phase model for a cylindrical polymer crystal, (a) Loops and tails are explicitly considered as an amorphous fraction in thermodynamic equilibrium with the crystalline fraction. The height of the amorphous layers is denotes by h, keeping the notation for m as the length of the crystalline stems. Both length scales are considered in units of statistical segments, (b) Illustration of the thermodynamic equilibrium system. Segments can be exchanged between two phases and the temperature is considered to be lower than equilibrium melting temperature...

The melting point must be equivalent in both samples at the extreme condition (infinite lamellar length), provided the native structure is of the same type, since the melting point (T ,) is thermodynamically defined as T = AH,JAS , where AH and AS are the enthalpy and the entropy of melting, re jectively. The 185 °C equilibrium melting temperature is rather amilar to the reported values... 

Partial melting can be studied by measuring the decrease in the degree of crystallinity (x) as a function of temperature in such a way as to avoid crystallization effects. The temperature at which x = 0 is of interest in that it is close to the hypothetical" thermodynamic equilibrium melting point (180). 

The thermodynamic equilibrium melting point of polymer crystals can be measured by means of DSC and small-angle X-ray diffraction. The following procedure is recommended for the measurement of the equilibrium melting temperature of a polymer crystal,... 

Equilibrium thermodynamic data are presented here to provide a base on which to judge the material on hand. It must always, however, be kept in mind that the actual samples analyzed are often not in equilibrium. Particularly, semicrystalline samples are not fully crystalline, do not contain perfect crystals that melt at the equilibrium melting temperature, and do not phase separate or mix when the thermodynamics are favorable (9-11). Similarly, many data must still be questioned as to their closeness to equilibrium or to the perfection of their extrapolation to equilibrium. 

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